Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2.

A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y.

B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs?

C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.

Suppose the long-run production function for a competitive firm is f(x₁,x₂)= min {3x1,2x2}. The cost
per unit of the first input is w₁ and the cost of the second input is w2.
a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level
of y.
b. Write down the formula and draw the graph of the firm's total cost function as a function of y,
using the conditional input demand functions. What is the relationship between the returns to
production scale and the behavior of the total costs?
c. Write down the formulas and draw the graphs of the average cost and marginal cost functions, as
functions of y.
Transcribed Image Text:Suppose the long-run production function for a competitive firm is f(x₁,x₂)= min {3x1,2x2}. The cost per unit of the first input is w₁ and the cost of the second input is w2. a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. b. Write down the formula and draw the graph of the firm's total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? c. Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.
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